1. Field of the Invention
This invention relates to an apparatus and method of growing single crystal for growing a silicon single crystal, which is used as a semiconductor material.
2. Description of Related Art
Generally, the Czochralski (CZ) method is widely employed for growing a single crystal.
FIG. 1 is a schematic cross-sectional view illustrating an apparatus and method of growing a single crystal on the basis of the CZ method. FIG. 1 indicates crucible, crystal, heater and heat shields. The crucible 1 consists of a graphite crucible 1a and a quartz crucible, which are concentrically positioned, and is fixed to the upper end of a rotatable and liftable pedestal 1c. A heater 2 is arranged at the outside of the crucible 1, and heat shields 3 and 4 are positioned at the outside of and below the heater 2, respectively.
In such an apparatus, a raw material for a crystal is charged into the crucible 1, and melted by tile heater 2 arranged at the outside of the crucible 1. Then, a seed 7 suspended from a wire 6 is immersed into the melted material L. While rotating, the seed 7 is pulled up, so that a single crystal 8 grows at the lower end of the seed 7.
When a single crystal is to be used as a semiconductor substrate, an impurity is usually added into the molten material L in the crucible 1, thereby adjusting the resistivity and conductivity type of the single crystal. Since such an impurity usually segregates toward the pulling direction of the single crystal 8, however, it is very difficult to obtain a crystal, in which an impurity concentration is uniform in the entire length of the single crystal 8 along the crystal growth direction.
This non-uniformity of an impurity comes from the segregation of the impurity in solidification. The ratio C.sub.S /C.sub.L, where C.sub.S and C.sub.L are the impurity concentration of the single crystal at the interface of the single crystal and the molten material L and the average impurity concentration of the molten material L, respectively, (i.e., the effective segregation coefficient Ke) is not 1.
It has been known to employ the melted layer method in order to suppress the segregation. FIG. 2 is a schematic cross-sectional view illustrating an apparatus for growing a single crystal according to the melted layer method. In this apparatus, the heater 2 is controlled so that a solid layer S formed at the bottom of the crucible 1 coexists with the melted lawyer L of the raw material formed above the solid layer, and under this coexisting state the single crystal 8 is grown by the same process as described in FIG. 1.
This melted layer method can be classified into the constant-thickness melted layer method and the variable-thickness melted layer method. The former is disclosed in Japanese Patent Application Publication (Kokoku) Nos. 34-8,242, 62-880, Japanese Patent Application Laid-Open (Kokai) No. 63-252,989, and the latter in Japanese Patent Application Laid-Open (Kokai) No. 61-205,691, In the constant-thickness melted layer method, the heater 2 is controlled during the pulling process so that the reduction of molten liquid caused by the pulling of the single crystal can be replenished by melting the solid layer S in order to keep the thickness of the melted layer L constant arid maintain the impurity concentration in the axial direction of single crystal more uniformly than the CZ method. And it possible that an impurity is continuously added during the growing in order to improve the uniformity. By contrast, in the variable-thickness melted layer method, the volume of the melted layer L is intentionally varied so that the impurity concentration in the axial direction of single crystal can be maintained at a constant value. The variable-thickness melted layer method is superior to the constant-thickness melted layer method from the viewpoint of realizing the non-segregation condition without the adding of impurity during the growing.
The principle of reducing the segregation in the above-described melted layer method can be described using a one-dimensional model shown in FIG. 3 in which the weight of the raw material initially charged in the crucible 1 (the initial charge amount) is "1" and the impurity concentration at a position of a weight ratio x measured from the upper surface of the raw material is expressed as C.sub.p (x).
When the weight ratio of the pulled crystal for the initial charge amount of 1 is f.sub.S, the weight ratio of the molten liquid is f.sub.L, the weight ratio of the solid at the lower portion in the crucible is f.sub.P, and f.sub.O =f.sub.S +f.sub.L, following equation (1) holds: EQU f.sub.O +f.sub.P =f.sub.S +f.sub.L +f.sub.P =1 (1)
The case that the impurity concentration C.sub.P of raw material is not zero (i.e., C.sub.P .noteq.0) will be described. In FIG. 3, the left side of the figure corresponds to the upper side of the crystal and the right side to the bottom of the solid layer.
FIG. 3(a) illustrates the concentration distribution obtained immediately after a raw material is charged into the crucible 1. In this state, the solid ratio f.sub.P is 1. FIG. 3(b) illustrates the concentration distribution obtained at the end of the initial melting process in which the upper portion of the raw material extending by the distance f.sub.L from the upper surface of the raw material is melted, and an impurity is added. In the figure, C.sub.O indicates the impurity concentration of the initial melted layer, and f.sub.O =f.sub.L.
FIG. 3 (c) illustrates the variation of the concentration obtained during the growth process. When the single crystal is pulled up by f.sub.S from the melted layer, the raw material positioned in the lower solid layer is melted (the melted portion is indicated by f.sub.L). In the figure, C.sub.L and C.sub.P indicate the impurity concentration of the melted layer and that of the lower solid layer, respectively.
When the impurity of an amount of C.sub.a .multidot..DELTA.f.sub.S is added while the single crystal is further pulled up by .DELTA.f.sub.S from f.sub.S as shown in FIG. 3(d), f.sub.L, C.sub.L and f.sub.P change to f.sub.L +.DELTA.f.sub.L, C.sub.L +.DELTA.C.sub.L, and f.sub.P +.DELTA.f.sub.P, respectively. In the figure, C.sub.S indicates the impurity concentration of the single crystal. In this case, the impurity amount of the region indicated by C.sub.L and C.sub.P before change, and C.sub.S and C.sub.L +.DELTA.C.sub.L after change (i.e., the region indicated by A in the figure) is constant. Therefore, following equation (2) holds: ##EQU1## where C.sub.S is defined by equation (3) below using the effective segregation coefficient Ke: EQU C.sub.S =Ke.multidot.C.sub.L ( 3)
By substituting equation (3) into equation (2) and omitting the second order small term, following equation (4) is obtained: ##EQU2##
In the usual CZ method, f.sub.p,.DELTA.f.sub.L +.DELTA.f.sub.S and C.sub.a are zero (f.sub.P =0, .DELTA.f.sub.L +f.sub.S =0 and C.sub.a =0), and therefore following equation (5) holds: ##EQU3## When equation (5) is substituted into equation (3), the following equation is obtained: EQU C.sub.S =Ke.multidot.C.sub.O .multidot.(1-f.sub.S).sup.Ke-1( 6)
In the melted layer method, dC.sub.L /df.sub.S and C.sub.P are zero (dC.sub.L /df.sub.S =0 and C.sub.P =0), and hence equation (7) is obtained from equation (4) in a similar manner: ##EQU4## This is the condition of realizing the non-segregation pulling. When this condition is applied to the constant-thickness melted layer method, df.sub.L /df.sub.S is zero (df.sub.L /df.sub.S =0), and consequently following equation (8) is obtained: EQU C.sub.a =Ke.multidot.C.sub.L =Ke.multidot.C.sub.O ( 8)
Then, the non-segregation condition can be realized by continuously adding the impurity.
In a case that the non-segregation condition is applied to the variable-thickness melted layer method, since the continuous addition of the impurity is not conducted in general C.sub.a is zero (C.sub.a =0), and hence following equation (9) is obtained from equation (7): ##EQU5##
The thickness of the melted layer is changed during the process of pulling the single crystal so as to satisfy equation (9), thereby realizing the non-segregation condition.
FIG. 3(e) illustrates the concentration distribution obtained when the lower solid is melted completely. In the constant-thickness melted layer method, after the solid layer S below the melted layer L is completely melted and f.sub.O becomes 1 (f.sub.O =1), the non-segregation condition is not satisfied, and the segregation starts in accordance with equation (6). By contrast, in the variable-thickness melted layer method, if following equation (10) is obtained from equation (9) holds until the end of the pulling, no segregation is attained to whole crystal. EQU f.sub.L =f.sub.LO -Ke.multidot.f.sub.S ( 10)
where f.sub.LO is the initial ratio of the melted layer with no crystal.
In the above-described melted layer method, the neck process, which is necessary to attain the non-dislocation, is carried out, and then the shoulder portion is formed by increasing the diameter of the single crystal to a predetermined value (about 154 mm for a 6-inch single crystal). While maintaining the predetermined diameter, thereafter, the single crystal is pulled up at a constant rate (about 1 mm/min. for a 6-inch single crystal), thereby forming a cylindrical single crystal.
In the pulling process of the above-described melted layer method, however, it is difficult to accurately control the melting amount of the solid layer S by the single heater 2, and also to stably obtain the desired solid layer S, because the sufficient temperature gradient cannot be achieved along the vertical direction in the crucible 1. As a result, there arise problems in that the impurity concentration of the molten material in the pulling process is difficult to be maintained at a constant value, and that the resistivity is not constant in the axial direction of the single crystal.
Furthermore, for example, in a stage wherein only a part of a raw material is melted and most of the raw material remains unmelted, the molten material often penetrates into the lower solid material in the crucible 1, which is relatively cool, and solidifies therein. This causes the volume of the solid material to expand so that the solid material pushes the wall of the crucible 1, with the result that the crucible 1 is broken and the molten material leaks therefrom. This brings another problem in that the apparatus is caused to break down.
As described above, in the melted layer method, the solid layer S exists at the lower portion of the crucible. Since experience shows that, when the percentage of the solid layer S is high (i.e., when the percentage of the melted layer L is low), the yield is high, a crucible must be taller than that used in the CZ method. In the CZ method, the ratio of the height to the diameter of a crucible is usually in the range from about 0.6 to about 0.8. However, in the melted layer method (ML method), the ratio needs to be 0.85 or more.
One of the important items of evaluating the single crystal 8 is the oxygen concentration of the single crystal 8. It is important to control the oxygen concentration, in the viewpoints of improving the mechanical strength of the single crystal 8 and removing contaminants such as heavy metals from the device active region of a single crystal wafer (Gettering). Generally, oxygen is incorporated from the quartz crucible 1b to the melted layer L as following formula (11): EQU 2SiO.sub.2 .fwdarw.2SiO+O.sub.2 ( 11)
Since, in the melted layer method, the solid layer S exists at the lower portion of the crucible 1 as described above, however, the contact area between the crucible 1 and the melted layer L is small as compared with the CZ method. This causes a problem in that the oxygen concentration of the pulled single crystal 8 is low.